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A305314 Second member m_2(n) of the Markoff triple MT(n) with largest member m(n) = A002559(n), and smallest member m_1(n) = A305313(n), for n >= 1. These triples are conjectured to be unique.

%I A305314 #6 Jun 28 2018 13:05:59
%S A305314 1,1,2,5,5,13,34,29,13,89,29,233,169,34,610,194,1597,985,433,194,89,
%T A305314 4181,169,10946,5741,433,2897,1325,233,28657,6466,1325,33461,75025,
%U A305314 7561,610,985,196418,43261,9077,195025,14701,514229,96557,2897,51641,9077,1597,37666,1346269,7561,1136689,14701,6466,3524578,646018,294685,135137,62210,5741
%N A305314 Second member m_2(n) of the Markoff triple MT(n) with largest member m(n) = A002559(n), and smallest member m_1(n) = A305313(n), for n >= 1. These triples are conjectured to be unique.
%C A305314 See A305313 for comments, and A002559 for references.
%F A305314 a(n) = m_2(n) is the fundamental proper solution y of the indefinite binary quadratic form x^2 - 3*m(n)*x*y + y^2, of discriminant D(n) = 9*m(n)^2 - 4 = A305312(n), representing -m(n)^2, for n >= 1, with x <= y. The uniqueness conjecture means that there are no other such fundamental solutions.
%e A305314 See A305313 for the first Markoff triples MT(n).
%Y A305314 Cf. A002559, A305312, A305313.
%K A305314 nonn
%O A305314 1,3
%A A305314 _Wolfdieter Lang_, Jun 25 2018